A211561 T(n,k) = number of nonnegative integer arrays of length n+k-1 with new values 0 upwards introduced in order, and containing the value k-1.

1, 1, 2, 1, 4, 5, 1, 7, 14, 15, 1, 11, 36, 51, 52, 1, 16, 81, 171, 202, 203, 1, 22, 162, 512, 813, 876, 877, 1, 29, 295, 1345, 3046, 4012, 4139, 4140, 1, 37, 499, 3145, 10096, 17866, 20891, 21146, 21147, 1, 46, 796, 6676, 29503, 72028, 106133, 115463, 115974, 115975

Offset

1,3

Comments

Table starts

....1.....1......1......1.......1........1........1.........1..........1

....2.....4......7.....11......16.......22.......29........37.........46

....5....14.....36.....81.....162......295......499.......796.......1211

...15....51....171....512....1345.....3145.....6676.....13091......24047

...52...202....813...3046...10096....29503....77078....183074.....401337

..203...876...4012..17866...72028...256565...810470...2300949....5957407

..877..4139..20891.106133..503295..2134122..8016373..26869727...81381744

.4140.21146.115463.649045.3513522.17337685.76199007.298009584.1046405027

Reading along antidiagonals seems to create A137650. - R. J. Mathar, Nov 29 2015

See also A133611. - Alois P. Heinz, Aug 30 2019

Links

R. H. Hardin, Table of n, a(n) for n = 1..9999

Formula

Empirical: T(n,k) = Sum_{j=k..n+k-1} stirling2(n+k-1,j)

Example

Some solutions for n=5, k=4:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....0....1....1....1....1....0....1....1....1....1....1....1....0
..1....2....2....0....0....2....2....0....1....2....2....2....2....0....2....1
..2....0....2....0....2....0....3....2....2....2....3....3....2....2....0....2
..3....1....3....1....3....2....1....3....3....2....1....3....3....2....1....2
..4....0....3....0....3....3....4....1....3....3....0....2....4....3....2....2
..5....3....3....2....4....4....2....1....2....2....1....0....4....3....3....2
..2....0....1....3....5....4....4....4....4....2....0....4....3....1....2....3

Crossrefs

Column 1 is A000110.

Column 2 is A058692(n+1).

Column 3 is A058681(n+1).

Row 2 is A000124.

Cf. A133611, A137650.

Sequence in context: A371686 A321000 A121289 * A134248 A248670 A080935

Adjacent sequences: A211558 A211559 A211560 * A211562 A211563 A211564

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 15 2012

Status

approved